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====== Running Example: Sales in a Data Warehouse ======

For the purpose of illustration this dissertation contains a
running example. It is used to demonstrate all concepts presented
in this document where it is applicable. Concepts where applying
this example does not make sense will be illustrated with their
own example---such as the necessary changes for applying the ideas
of this dissertation to data streams.

Assume there is a large publishing company maintaining a data
warehouse for both strategic and operational decision making. The
data warehouse contains a vast set of data mainly concerning the
sales of the company's products---books, magazines, journals and
on-line articles. Data about transactions with printing companies
form another large part of the data warehouse.

The company has optimised its data warehouse for OLAP but not yet
for data mining. Later sections of this dissertation will present
ways the company can use to improve its performance of \kdd
analyses in terms of quality and speed.

\begin{figure}
\centering
\includegraphics[width=12cm]{weltkarte.eps}
\caption{network of a globally operating company}
\label{globalmap}
\end{figure}

The publishing company is globally operating. Therefore, there are
six major locations that administrate the operations of smaller
units. Each of these six administration centres operates a data
warehouse that contains the data of those units that report to
that centre of administration.

The location of the company's headquarter coincides with one of
the centres of administration.

Figure \ref{globalmap} shows the distribution of the six major
locations, which are symbolised by rectangles with crosses, and
their affiliated units, which are represented by circles, around
the globe. Arrows and lines denote the amount of traffic of data
exchange between locations.

\begin{figure}
\centering
\includegraphics[width=12cm]{sales_golfarelli.eps}
\caption{schema of cube sales in Golfarelli notation}
\label{sales_golfarelli}
\end{figure}

The global data warehouse and all local data warehouses share the
same schema. Each data warehouse contains several cubes but the
`sales' cube is by far the cube having the highest number of
tuples---its size exceeds the sum of the sizes of all other cubes.
Table \ref{schema} shows the relational schema of the tables that
store the data of the `sales' cube.

The schema of the `sales' cube is a starflake schema as it is
shown in figure \ref{sales_golfarelli}. Figure
\ref{sales_golfarelli} uses the notation of data warehouse schemas
introduced by Golfarelli in \cite{golfarelli}. The `sales' cube
has two measurements, namely the quantity of items sold and the
price per sold unit. The cube has the four dimensions
//product//, //customer//, //time//, and //unit//.

Products are assigned to product groups which themselves are
hierarchically ordered in groups and sub-groups---the number of
levels in this hierarchy is potentially unlimited. Hence,
dimension //product// has a hierarchy with a recursion.

Dimension //customer// is structured by the location of the
customer and alternatively by the type of customer. There are the
two types //individual// and //corporate// customer, where
the group of corporate customers includes all kind of
organisations such as companies but also incorporated societies or
non-government organisations. The company delivers books and other
printed material only by mail. On-line purchases require a
previous registration in which a valid address is required. Thus,
there are no anonymous sales.

Dimension //time// is organised conventionally except years are
omitted for simplicity.

A roll-up operation in any dimension causes the quantity
measurement being summed-up while an average price per unit is
determined.

The data warehouse schema is realised in a set of relations of a
relational database. Table \ref{schema} contains the schema of
these relations.

\begin{table}
  \centering
  \begin{tabular}{|lp{95mm}|}
    \hline
^Relations & {\tt sales(units, priceperunit, timestamp, \it{prid}, \it{shopid}, \it{cid})} \\
    & {\tt product(\underline{prid}, name) } \\
    & {\tt productgroup(\underline{groupid}, groupname), {\it ispartof}} \\
    & {\tt isproductofgroup(\underline{\it{prid}},
\underline{\it{groupid}})} \\
    & {\tt unit(\underline{shopid}, name, citycode, statecode)} \\
    & {\tt customer(\underline{cid}, name, customertype, citycode, statecode)} \\ & \\
    \hline
    Inclusion & {\tt sales(prid) $\subseteq$ product(prid)} \\
    Dependencies & {\tt isproductofgroup(prid) $\subseteq$ product(prid)} \\
    & {\tt isproductofgroup(groupid) $\subseteq$ productgroup(groupid)} \\
    & {\tt productgroup(ispartof) $\subseteq$ productgroup(groupid)} \\
    & {\tt sales(cid) $\subseteq$ customer(cid)} \\
    \hline
    \hline
    Legend& relations are shown in the form \\
    &{\tt <relation name>(<attribute
    list>)}\\
    & attributes of the primary key are underlined,
    attributes of foreign keys are written in italics\\
    \hline
  \end{tabular}
  \caption{relational schema of the running example}\label{schema}
  \medskip

\end{table}

\begin{table}
  \centering
  \begin{tabular}{|c|c|}
  \hline
  \emph{prid}&\emph{name}\\
  \hline
  1&Theory and Implementation of Anticipatory Data Mining\\
  \hline
  \end{tabular}
  \caption{Sample Entries of Table \emph{product}}
  \label{sampleProduct}
\end{table}



  \begin{tabular}{|c|c|c|}

^groupid^groupname^ispartof^ 
^1|book|NULL| 
^2|belletristic|1|
^3|scientificmonography|1|
^4|article|NULL|
^5|webarticle|4|
^6|online journal|NULL|
Sample Entries of Table //productgroup//

\end{table}

Smaller units daily send their data about sales of that day to the
centre of administration they report to. There, a large
ETL\index{ETL} (Extract-Transform-Load) process inserts these data
into the local data warehouse.

The amount of daily arriving data each centre of administration
exceeds 1GB.

Beside OLAP-queries the company regularly performs data mining
analyses using the data that is kept in the data warehouse. The
types of these analyses are two-fold: A lot of these analyses are
re-runs of former analyses to validate their results while others
are completely new.

Both analysts residing in the headquarter and local analysts use
the contents of the data warehouses for data mining analyses
regularly. The analyses of local analysts might require all data
stored in all data warehouses or specific parts of it. Especially,
an analysis is not limited to the content of a local data
warehouse.

To be more specific, suppose the following analyses are about to
be performed on the current date:

  - The number of sale transactions of a specific publication is varying
  temporally. Many factors such as publication type or reputation
  of the author influence the demand for a specific publication.

  The publishing company uses multi-variate linear regression method
  to estimate the current demand of their publications. The resulting
  regression model predicts the number of purchases for each publication.
  It is a model of the life-cycle of a given type of publication.
  As the preferences of customers might change, the company regularly
  re-constructs the linear regression model to cope with
  changes in customer purchase behaviour.

  * Customers can buy online articles individually or as part of an annual subscription of an online journal. An annual subscription is implemented as a separate product. The publishing company wants to find a model to predict which subscriber will not extend one's subscription. The company pays much attention to those customers because the regular turnover from subscriptions offers high margins. Additionally, retaining unsatisfied customers is known to be generally cheaper than acquiring new customers.

  * The marketing division compiles catalogues and hand-outs for specific customer segments that have not been identified, yet. An analyst of the company shall find a suitable segmentation ofcustomers. Clustering is his preferred method to complete this task.
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